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Spectral Gap Optimization for Enhanced Adiabatic State Preparation

Kshiti Sneh Rai1,2,*, Jin-Fu Chen1,2,†, Patrick Emonts1,2,3,4,‡, and Jordi Tura1,2

  • *Contact author: ksrai@lorentz.leidenuniv.nl
  • †Contact author: jinfuchen@lorentz.leidenuniv.nl
  • ‡Contact author: patrick.emonts@uni-ulm.de
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Phys. Rev. Lett. 135, 090602 – Published 29 August, 2025

DOI: https://doi.org/10.1103/cslt-x32n

Abstract

The preparation of nontrivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this Letter, we propose an efficient method to adiabatically prepare tensor network states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNSs, through examples of random TNSs in one dimension, AKLT (Affleck-Kennedy-Lieb-Tasaki), and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.

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Phys. Rev. Lett. 135, 090602– Published 29 August, 2025
  • Received 18 October 2024
  • Revised 5 March 2025
  • Accepted 10 July 2025
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